LASSO-based multivariate linear profile monitoring

Abstract

In many applications of manufacturing and service industries, the quality of a process is characterized by the functional relationship between a response variable and one or more explanatory variables. Profile monitoring is for checking the stability of this relationship over time. In some situations, multiple profiles are required in order to model the quality of a product or process effectively. General multivariate linear profile monitoring is particularly useful in practice due to its simplicity and flexibility. However, in such situations, the existing parametric profile monitoring methods suffer from a drawback in that when the profile parameter dimensionality is large, the detection ability of the procedures commonly used T 2 -type charting statistics is likely to decline substantially. Moreover, it is also challenging to isolate the type of profile parameter change in such high-dimensional circumstances. These issues actually inherit from those of the conventional multivariate control charts. To resolve these issues, this paper develops a new methodology for monitoring general multivariate linear profiles, including the regression coefficients and profile variation. After examining the connection between the parametric profile monitoring and multivariate statistical process control, we propose to apply a variable-selection-based multivariate control scheme to the transformations of estimated profile parameters. Our proposed control chart is capable of determining the shift direction automatically based on observed profile data. Thus, it offers a balanced protection against various profile shifts. Moreover, the proposed control chart provides an easy but quite effective diagnostic aid. A real-data example from the logistics service shows that it performs quite well in the application.

Statistical Perspectives on “Big Data”

“…Zou and Qiu (2009) considered the least absolute shrinkage and selection operator (LASSO) test statistic of Tibshirani (1996) combined with a multivariate exponentially weighted moving average (EWMA) control chart to quickly identify process changes and to identify the shifted mean components. Zou et al (2012) considered the use of the LASSO statistic applied to profile monitoring. Zou et al (2011) developed a LASSO based diagnostic framework for statistical process control that applies to high dimensional data sets.…”

Process Yield for Multivariate Linear Profiles with One-sided Specification Limits

“…In this section, two examples are used to illustrate the applicability of our proposed method.Example The multivariate linear profile model from the logistic service is considered. Two response variables are obtained as follows: y 1 denotes the number of jobs per day in the company's ports, and y 2 denotes the daily average time length to complete a job.…”

Developing a univariate approach to phase-I monitoring of fuzzy quality profiles

“…Hosseinifard et al (2011) developed three monitoring methods based on artificial neural networks to monitor linear profiles. Zou et al (2012) developed a methodology for monitoring general multivariate linear profiles, including the regression coefficients and profile variation in the basis of applying the variable-selection-based multivariate control scheme to the transformations of estimated profile parameters. Amiri et al (2012) proposed a dimension reduction method to overcome the dimensionality problem of some of the methods on phase II monitoring of multiple linear regression profile.…”